Template:Graph families defined by their automorphisms

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Graph families defined by their automorphisms
distance-transitive<math>\rightarrow</math>distance-regular<math>\leftarrow</math>strongly regular
<math>\downarrow</math>
symmetric (arc-transitive)<math>\leftarrow</math>t-transitive, t ≥ 2
<math>\downarrow</math>(if connected)
vertex- and edge-transitive<math>\rightarrow</math>edge-transitive and regular<math>\rightarrow</math>edge-transitive
<math>\downarrow</math><math>\downarrow</math><math>\downarrow</math>
vertex-transitive<math>\rightarrow</math>regular<math>\rightarrow</math>(if bipartite)
biregular
<math>\uparrow</math>
Cayley graphskew-symmetricasymmetric